The general objective of this research is to establish quantitative criteria for judging the potential for a therapeutic gain from alternative fractionation schemes in radiotherapy. More specifically, these studies aim at establishing estimates, for a given normal tissue, of (1) the smallest fractional dose at which a detectable increase in sparing occurs, and (2) the shortest interafraction interval for complete Elkind repair. Emphasis is placed on the application of applied mathematics to problems in experimental design and analysis, in which the objective is obtaining dose-response curves from in vivo assays of acute and late radiation injury. In particular, techniques are sought for obtaining quantitative, dose-response and repair kinetics parameters from qualitavie assays of early and late responses. These studies could ultimately provide guidelines for the use of hyperfractionated radiotherapy, through an understanding of the sites where it would be most beneficial and through and appreciation of the limits imposed on the number of daily treatments by the necessity for complete Elkind repair.